It appears you've gathered most of the relevant information, but a critical element is missing. The surface represented is parameterized by... and has a normal vector corresponding to this representation with a specified norm. Thus, the integral of... is...
There were 30 adults and 10 children, totaling 40 attendees. Just sum them together.
Let the number be x. The equation x/5 - 17 = 48 leads to (x - 85)/5 = 48. Multiplying gives x - 85 = 240, so x = 240 + 85, resulting in x = 325.
